1536edo: Difference between revisions

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{{~~EDO~~ intro~~|1536~~}} Its adjacent step is known as ''[[heptamu]]'' (seventh MIDI-resolution unit, ''[[7mu]]'', 2<sup>7</sup> = 128 equal divisions of the [[12edo]] semitone). The internal data structure of the 7mu requires two bytes, with the first bits of each byte reserved as a flags to indicate the byte's status as data, and one bit in the first byte to indicate the sign (+ or −) showing the direction of the pitch-bend up or down, and 6 other bits which are not used. The first data byte transmitted is the Least Significant Byte (LSB), equivalent to a fine-tuning. The second data byte transmitted is the Most Significant Byte (MSB), equivalent to a coarse-tuning.

== Theory ==

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If we do use it for the 5-limit, then {{val| 1536 '''2434''' '''3566''' }} (1536b [[val]]) and {{val| 1536 '''2435''' '''3567''' }} (1536c val) are worth considering, but 1536b is [[enfactoring|enfactored]] through the 17-limit (see [[768edo]]), leaving us with 1536c alone. It [[tempering out|tempers out]] 6115295232/6103515625 ([[vishnuzma]]) and {{monzo| 169 -111 3 }} in the 5-limit; [[250047/250000]], 134217728/133984375, and 12111126300875/12050326889856 in the 7-limit.

=== As a tuning standard ===

A step of 1536edo is known as a ''[[heptamu]]'' (seventh MIDI-resolution unit, 7mu, {{nowrap|2<sup>7</sup> {{=}} 128}} equal divisions of the [[12edo]] semitone). The internal data structure of the 7mu requires two bytes, with the first bits of each byte reserved as flags to indicate the byte's status as data, and one bit in the first byte to indicate the sign (+ or −) showing the direction of the pitch-bend up or down, and 6 other bits which are not used. The first data byte transmitted is the Least Significant Byte (LSB), equivalent to a fine-tuning. The second data byte transmitted is the Most Significant Byte (MSB), equivalent to a coarse-tuning.

=== Odd harmonics ===

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** [[98304edo]] (13mu tuning)

** [[196608edo]] (14mu tuning)

== External links ==

* [http://tonalsoft.com/enc/number/7mu.aspx 7mu / heptamu] on [[Tonalsoft Encyclopedia]]

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 {{Infobox ET}}
-{{EDO intro|1536}} Its adjacent step is known as ''[[heptamu]]'' (seventh MIDI-resolution unit, ''[[7mu]]'', 2<sup>7</sup> = 128 equal divisions of the [[12edo]] semitone). The internal data structure of the 7mu requires two bytes, with the first bits of each byte reserved as a flags to indicate the byte's status as data, and one bit in the first byte to indicate the sign (+ or &minus;) showing the direction of the pitch-bend up or down, and 6 other bits which are not used. The first data byte transmitted is the Least Significant Byte (LSB), equivalent to a fine-tuning. The second data byte transmitted is the Most Significant Byte (MSB), equivalent to a coarse-tuning.
+{{ED intro}}
 == Theory ==
@@ Line 6: / Line 6: @@
 If we do use it for the 5-limit, then {{val| 1536 '''2434''' '''3566''' }} (1536b [[val]]) and {{val| 1536 '''2435''' '''3567''' }} (1536c val) are worth considering, but 1536b is [[enfactoring|enfactored]] through the 17-limit (see [[768edo]]), leaving us with 1536c alone. It [[tempering out|tempers out]] 6115295232/6103515625 ([[vishnuzma]]) and {{monzo| 169 -111 3 }} in the 5-limit; [[250047/250000]], 134217728/133984375, and 12111126300875/12050326889856 in the 7-limit.
+=== As a tuning standard ===
+A step of 1536edo is known as a ''[[heptamu]]'' (seventh MIDI-resolution unit, 7mu, {{nowrap|2<sup>7</sup> {{=}} 128}} equal divisions of the [[12edo]] semitone). The internal data structure of the 7mu requires two bytes, with the first bits of each byte reserved as flags to indicate the byte's status as data, and one bit in the first byte to indicate the sign (+ or −) showing the direction of the pitch-bend up or down, and 6 other bits which are not used. The first data byte transmitted is the Least Significant Byte (LSB), equivalent to a fine-tuning. The second data byte transmitted is the Most Significant Byte (MSB), equivalent to a coarse-tuning.
 === Odd harmonics ===
@@ Line 28: / Line 31: @@
 ** [[98304edo]] (13mu tuning)
 ** [[196608edo]] (14mu tuning)
+== External links ==
+* [http://tonalsoft.com/enc/number/7mu.aspx 7mu / heptamu] on [[Tonalsoft Encyclopedia]]